Q.
Equal volumes of two immiscible liquids of densities $\rho$ and $2\ \rho$ are filled in a vessel as shown in figure. Two small holes are made at depth $h/2\ $ and $3\ h/2$ from the surface of lighter liquid. If $v_{1}$ and $v_{2}$ are the velocities of efflux at these two holes, then $v_{1}/v_{2}$ is
A) $\frac{1}{\sqrt{2}}$
B) $\frac{1}{4}$
C) $\frac{1}{2}$
D) $\frac{1}{2\sqrt{2}}$
Explanation
(a) Here $v_{1} = \sqrt{2g(h/2)} = \sqrt{gh}$ …(i)
Using Bernoulli’s theorem, we have
$p_{a} + \rho\ gh + 2pg(h/2) = p_{a} + \frac{1}{2}(2\rho)v_{2}^{2}$
Or $v_{2} = \sqrt{2gh}$ …(ii)
$\therefore\frac{v_{1}}{v_{2}} = \frac{1}{\sqrt{2}}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.